The goal of this project is to produce a carefully prepared and widely acceptable review (in book form) of neuron biophysics which will facilitate communication between the fields of electrophysiology, bioengineering, and applied mathematics. This review will attempt to reinforce the emerging trend in biophysics toward the direct calculation of experimental results from fundamental principles and away from simple "model-making." Although a substantial component of analytical research is anticipated in the course of this work, support is being requested under the National Library of Medicine's Publication Grant Program.